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A Review of Prolate Spheroidal Wave Functions from the Perspective of Spectral Methods

A Review of Prolate Spheroidal Wave Functions from the Perspective of Spectral Methods
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Year:    2017

Author:    Li-Lian Wang

Journal of Mathematical Study, Vol. 50 (2017), Iss. 2 : pp. 101–143

Abstract

This paper is devoted to a review of the prolate spheroidal wave functions (PSWFs) and their variants from the viewpoint of spectral ⁄ spectral-element approximations using such functions as basis functions. We demonstrate the pros and cons over their polynomial counterparts, and put the emphasis on the construction of essential building blocks for efficient spectral algorithms.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v50n2.17.01

Journal of Mathematical Study, Vol. 50 (2017), Iss. 2 : pp. 101–143

Published online:    2017-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    43

Keywords:    Prolate spheroidal wave functions and their generalisations time-frequency concentration problem bandlimited functions finite Fourier ⁄ Hankel transforms quasi-uniform grids well-conditioned prolate collocation scheme prolate-Galerkin method spectral accuracy.

Author Details

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